Using a pot, add oil and allow it to get hot over medium or medium-high heat.
On a surface, mix together the flour (2 cups), baking soda, butter, and salt. Mix until butter is distributed throughout the ingredients.
Add the egg and egg yolk. Also add the orange liquor/juice. Knead until the ingredients have absorbed them.
While kneading, add the white wine. Add a bit more flour if needed to get good consistency. The dough should be smooth and not sticky.
Roll the dough out on a floured surface, you want it to be thin. Cut into little strips (about 2x4 inches). Next, drop them into the hot oil and cook them in batches for a few minutes. Make sure to turn them half way through so they get evenly colored.
Cook all of your chiacciere in batches. Once drained on a paper towel lined plate, let them cool slightly. Sprinkle on some confectioners sugar over the top!